Trace Lasso Research Articles

A Novel Improved Dragonfly Algorithm-Based Structural Damage Identification Approach Using Flexibility Assurance Criterion and Trace Lasso

Aiming to enhance the accuracy, stability, and noise robustness of swarm intelligence-based algorithms for structural damage identification (SDI), a novel improved dragonfly algorithm (IDA) is proposed. The IDA integrates the dragonfly algorithm (DA) with three key strategies including enhanced Lévy flight, optimal solution bidirectional search, and greedy preservation. These strategies are introduced to enhance the exploration capability of the original DA and improve the IDA’s capacity to obtain global optima. An objective function is defined using frequency change ratio and flexibility assurance criterion (FAC). Additionally, trace sparse regularization is also incorporated into the objective function since most of the damages in structures tend to be sparsely distributed, so that a sparse result is ensured to improve SDI accuracy. To evaluate the performance of the proposed algorithm, a comparison of the original DA and IDA is conducted using four benchmark functions. The results demonstrate that the proposed algorithm achieves improved convergent rate and accuracy. Furthermore, numerical simulations are performed on a 10-element simply-supported beam and a 31-element planar truss to validate the effectiveness and efficiency of the proposed algorithm in SDI. Significantly, the utilization of IDA instead of DA leads to a substantial reduction in the average calculated relative error for the truly damaged element within the considered damage cases of the simply-supported beam, decreasing from 13.05% to 6.15%. Moreover, an experimental simply-supported beam structure with several assumed damage cases is fabricated in the laboratory. The experimental results further confirm the robustness and capability of the proposed method in real-world SDI applications.

Trace Lasso Regularization for Adaptive Sparse Canonical Correlation Analysis via Manifold Optimization Approach

Trace Lasso Regularization for Adaptive Sparse Canonical Correlation Analysis via Manifold Optimization Approach

A Manifold Laplacian Regularized Semi-Supervised Sparse Image Classification Method With a Variant Trace Lasso Norm

Since the cost of labeling data is getting higher and higher, we hope to make full use of the large amount of unlabeled data and improve image classification effect through adding some unlabeled samples for training. In addition, we expect to uniformly realize two tasks, namely the clustering of the unlabeled data and the recognition of the query image. We achieve the goal by designing a novel sparse model based on manifold assumption, which has been proved to work well in many tasks. Based on the assumption that images of the same class lie on a sub-manifold and an image can be approximately represented as the linear combination of its neighboring data due to the local linear property of manifold, we proposed a sparse representation model on manifold. Specifically, there are two regularizations, i.e., a variant Trace lasso norm and the manifold Laplacian regularization. The first regularization term enables the representation coefficients satisfying sparsity between groups and density within a group. And the second term is manifold Laplacian regularization by which label can be accurately propagated from labeled data to unlabeled data. Augmented Lagrange Multiplier (ALM) scheme and Gauss Seidel Alternating Direction Method of Multiplier (GS-ADMM) are given to solve the problem numerically. We conduct some experiments on three human face databases and compare the proposed work with several state-of-the-art methods. For each subject, some labeled face images are randomly chosen for training for those supervised methods, and a small amount of unlabeled images are added to form the training set of the proposed approach. All experiments show our method can get better classification results due to the addition of unlabeled samples.

A hybrid ant lion optimizer with improved Nelder–Mead algorithm for structural damage detection by improving weighted trace lasso regularization

Structural damage detection is the kernel technique in deploying structural health monitoring. The structural damage–detection technique using heuristic algorithms has been developed at an astounding pace over the past years. However, some existing structural damage–detection methods are prone to easily fall into the local optimum and to be unstable when they are applied to complex structures. In order to make full use of advantages of heuristic algorithms and overcome abovementioned shortcomings, a hybrid algorithm, which combines the ant lion optimizer with an improved Nelder–Mead algorithm, is proposed to solve the constrained optimization problem of complex structural damage detection. First, an objective function is established for damage identification using structural modal parameters, that is, frequencies and mode shapes. The solution to the objective function is accurately attained by a newly improved weighted trace lasso which can improve the computing performance and stability of procedure and reduce randomness of weighted coefficients. After assessing the computing performance of the proposed hybrid algorithm using three classical mathematical benchmark functions, two structural damage–detection numerical simulations and a laboratory verification are then conducted to fully assess the structural damage–detection capability of the proposed method. Meanwhile, the equivalent element stiffness-reduction model is introduced to estimate the real damage severities of cracks which are created in laboratory structures and to compare with the structural damage–detection results by the proposed method. The illustrated results show that the proposed hybrid algorithm can locate damage and quantify damage severity more accurately and stably with a good robustness to noise.

A Trace Lasso Regularized Robust Nonparallel Proximal Support Vector Machine for Noisy Classification

Generalized eigenvalue proximal support vector machine (GEPSVM) and its improvement IGEPSVM are excellent nonparallel classification methods due to their excellent generalization. However, all of them adopt the square L 2 -norm metric to implement their empirical risk or penalty, which is sensitive to noise and outliers. Moreover, in many real-world learning tasks, it is a significant challenge for GEPSVMs when the data appears highly correlated. To alleviate the above issues, in this paper, we propose a novel trace lasso regularized robust nonparallel proximal support vector machine (RNPSVM) for noisy classification. Compared with GEPSVMs, our RNPSVM enjoys the following advantages. First, the empirical risk of RNPSVM is implemented by the robust L 1 -norm metric with a maximum margin criterion. Namely, it aims to maximize the L 1 -norm inter-class distance dispersion while minimizing the L 1 -norm intra-class distance dispersion simultaneously. Second, to capture the sparsity and the underlying correlation of data, a trace lasso (adaptive norm-based training data) is further introduced to regularize RNPSVM. Third, an iterative algorithm is designed to solve the maximization optimization problem of RNPSVM, whose convergence is guaranteed theoretically. The extensive experimental results on both synthetic and real-world noisy datasets demonstrate the effectiveness of RNPSVM.

Structural damage detection via combining weighted strategy with trace Lasso

With the rapid development of computation technologies, swarm intelligence–based algorithms become an innovative technique used for addressing structural damage detection issues, but traditional swarm intelligence–based structural damage detection methods often face with insufficient detection accuracy and lower robustness to noise. As an exploring attempt, a novel structural damage detection method is proposed to tackle the above deficiency via combining weighted strategy with trace least absolute shrinkage and selection operator (Lasso). First, an objective function is defined for the structural damage detection optimization problem by using structural modal parameters; a weighted strategy and the trace Lasso are also involved into the objection function. A novel antlion optimizer algorithm is then employed as a solution solver to the structural damage detection optimization problem. To assess the capability of the proposed structural damage detection method, two numerical simulations and a series of laboratory experiments are performed, and a comparative study on effects of different parameters, such as weighted coefficients, regularization parameters and damage patterns, on the proposed structural damage detection methods are also carried out. Illustrated results show that the proposed structural damage detection method via combining weighted strategy with trace Lasso is able to accurately locate structural damages and quantify damage severities of structures.

Image segmentation by adaptive nonconvex local and global subspace representation

We formulate image segmentation as subspace clustering of image feature vectors. We propose a subspace representation model using a nonconvex extension of trace Lasso and a nonconvex approximation of rank function to regularize the subspace representation. The proposed model can adaptively capture the local and the global structures of the subspace representation so that the subspace representation can reveal the real subspace structure of the data and obtains excellent clustering performance. Experimental results show that the proposed model is better than the previous models in clustering and natural image segmentation.

L1-norm and maximum margin criterion based discriminant locality preserving projections via trace Lasso

Discriminant locality preserving projections based on maximum margin criterion (DLPP/MMC) is a useful feature extraction method since it has shown good performances in pattern recognition. The conventional DLPP/MMC, however, is not robust to noises and outliers since its objective function is based on L2-norm. In this paper, we propose a novel L1-norm and maximum margin criterion based discriminant locality preserving projections via trace Lasso (DLPP/MMC-L1TL). L1-norm rather than L2-norm is used in the formulation of DLPP/MMC-L1TL, which makes it be robust to noises and outliers. Besides, in order to improve the performance of DLPP/MMC-L1TL further, we use trace Lasso to regularize the basis vectors. Trace Lasso, which can balance L1-norm and L2-norm and consider sparsity and correlation of data simultaneously, is a recently proposed norm. An iterative procedure for solving DLPP/MMC-L1TL is also proposed in this paper. The experiment results on some data sets demonstrate the effectiveness of DLPP/MMC-L1TL.